A process for operating of an internal combustion engine running on fuel that is both externally ignitible and self-ignitible, especially gasoline, the operating region of the engine including self-ignition or compression-ignition regions and external-ignition or sparkignition regions, and a high compression ratio suitable for self-ignition of the fuel being provided, at least in compression-ignition regions, and fuel combustion being initiated by self-ignition of the fuel-air mixture in compression-ignition regions and by spark-ignition of the fuel-air mixture in spark-ignition regions, and part-load operation being assigned to the compression-ignition region, whilst full-load operation and/or operating modes with high engine load as well as cold starts are assigned to the sparkignition region.